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Modelling informative time points: an evolutionary process approach

Author

Listed:
  • Andreia Monteiro

    (University of Minho)

  • Raquel Menezes

    (University of Minho)

  • Maria Eduarda Silva

    (University of Porto)

Abstract

Real time series sometimes exhibit various types of “irregularities”: missing observations, observations collected not regularly over time for practical reasons, observation times driven by the series itself, or outlying observations. However, the vast majority of methods of time series analysis are designed for regular time series only. A particular case of irregularly spaced time series is that in which the sampling procedure over time depends also on the observed values. In such situations, there is stochastic dependence between the process being modelled and the times of the observations. In this work, we propose a model in which the sampling design depends on all past history of the observed processes. Taking into account the natural temporal order underlying available data represented by a time series, then a modelling approach based on evolutionary processes seems a natural choice. We consider maximum likelihood estimation of the model parameters. Numerical studies with simulated and real data sets are performed to illustrate the benefits of this model-based approach.

Suggested Citation

  • Andreia Monteiro & Raquel Menezes & Maria Eduarda Silva, 2021. "Modelling informative time points: an evolutionary process approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 364-382, June.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:2:d:10.1007_s11749-020-00722-2
    DOI: 10.1007/s11749-020-00722-2
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    References listed on IDEAS

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    1. Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    2. P. Diggle & M. G. Kenward, 1994. "Informative Drop‐Out in Longitudinal Data Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 49-73, March.
    3. Kristensen, Kasper & Nielsen, Anders & Berg, Casper W. & Skaug, Hans & Bell, Bradley M., 2016. "TMB: Automatic Differentiation and Laplace Approximation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i05).
    4. Ryu, Duchwan & Sinha, Debajyoti & Mallick, Bani & Lipsitz, Stuart R. & Lipshultz, Steven E., 2007. "Longitudinal Studies With Outcome-Dependent Follow-up: Models and Bayesian Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 952-961, September.
    5. Yu Liang & Wenbin Lu & Zhiliang Ying, 2009. "Joint Modeling and Analysis of Longitudinal Data with Informative Observation Times," Biometrics, The International Biometric Society, vol. 65(2), pages 377-384, June.
    6. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    7. P. A. W Lewis & G. S. Shedler, 1979. "Simulation of nonhomogeneous poisson processes by thinning," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 403-413, September.
    8. Wang, Zhu, 2013. "cts: An R Package for Continuous Time Autoregressive Models via Kalman Filter," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i05).
    Full references (including those not matched with items on IDEAS)

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